Exhibit 99.1

Sunesis Pharmaceuticals Announces Closing of

$40 Million in Previously Announced Royalty and Debt Financings

Company Funded Through VALOR Unblinding in 2014

SOUTH SAN FRANCISCO, Calif., (September 20, 2012) – Sunesis Pharmaceuticals, Inc. (NASDAQ: SNSS) today announced the closing of two previously disclosed financings. Royalty Pharma has invested $25.0 million under its royalty arrangement with Sunesis, and, in a separate transaction, a syndicate of lenders have funded the second tranche of $15.0 million under their $25.0 million loan facility with the company.

The loan facility, announced in October 2011, is led by Oxford Finance and partnered with Silicon Valley Bank and Horizon Technology Finance Corporation. The transaction with Royalty Pharma was first announced in March 2012.

Both financings were triggered by the decision to implement a one-time, 225-patient sample size increase to Sunesis’ VALOR trial, a Phase 3, multinational, randomized, double-blind, placebo-controlled, pivotal clinical trial of vosaroxin in combination with cytarabine in first relapsed or refractory acute myeloid leukemia (AML). Sunesis currently holds all worldwide commercial rights to its vosaroxin product.

Sunesis anticipates using the funds to support the clinical development activities related to VALOR as well as other working capital and general corporate purposes.

“These financings, together with our existing cash and investments, will fund Sunesis’ execution of the VALOR trial through full data readout in the first half of 2014,” said Eric Bjerkholt, Executive Vice President, Corporate Development and Finance, Chief Financial Officer of Sunesis. “The strength of our balance sheet enables us to prosecute VALOR to unblinding and continue preparations for related regulatory filings and commercial launch. We appreciate the support of Royalty Pharma and our lender group, and their continued confidence in vosaroxin, VALOR and Sunesis.”

About VALOR

VALOR is a Phase 3, randomized, double-blind, placebo-controlled, pivotal trial in patients with first relapsed or refractory AML. The trial’s target enrollment is 675 patients at more than 110

leading sites in the U.S., Canada, Europe, Australia and New Zealand. The VALOR trial is currently enrolling patients, who are randomized one to one to receive either vosaroxin on days one and four in combination with cytarabine daily for five days, or placebo in combination with cytarabine. The trial’s primary endpoint is overall survival. For more information on the VALOR trial, please visit www.valortrial.com.

About Vosaroxin

Vosaroxin is a first-in-class anti-cancer quinolone derivative (AQD), a class of compounds that has not been used previously for the treatment of cancer. Vosaroxin both intercalates DNA and inhibits topoisomerase II, resulting in replication-dependent, site-selective DNA damage, G2 arrest and apoptosis. Both the U.S. Food and Drug Administration (FDA) and European Commission have granted orphan drug designation to vosaroxin for the treatment of acute myeloid leukemia. Additionally, vosaroxin has been granted fast track designation by the FDA for the potential treatment of relapsed or refractory acute myeloid leukemia in combination with cytarabine.

About AML

AML is a rapidly progressing cancer of the blood characterized by the uncontrolled proliferation of immature blast cells in the bone marrow. The American Cancer Society estimates there will be approximately 13,780 new cases of AML and 10,200 deaths from AML in the U.S. in 2012. Additionally, it is estimated that the prevalence of AML across major global markets (U.S., France, Germany, Italy, Spain, United Kingdom, and Japan) is over 50,000. AML is generally a disease of older adults, and the median age of a patient diagnosed with AML is about 67 years. AML patients with relapsed or refractory disease and newly diagnosed AML patients over 60 years of age with poor prognostic risk factors typically die within one year, resulting in an acute need for new treatment options for these patients.

About Sunesis Pharmaceuticals

Sunesis is a biopharmaceutical company focused on the development and commercialization of new oncology therapeutics for the treatment of solid and hematologic cancers. Sunesis has built a highly experienced cancer drug development organization committed to advancing its lead product candidate, vosaroxin, in multiple indications to improve the lives of people with cancer. For additional information on Sunesis, please visit http://www.sunesis.com.

SUNESIS and the logos are trademarks of Sunesis Pharmaceuticals, Inc.

This press release contains forward-looking statements, including statements related to the sufficiency of Sunesis’ cash and investments to fund the company’s operations and the VALOR trial through its planned unblinding in the first half of 2014, Sunesis’ expectations regarding the completion and anticipated use of proceeds from the disclosed financings and the design, conduct, progress and results of the VALOR trial. Words such as “anticipates,” “will,” “enables,” “continued” and similar expressions are intended to identify forward-looking statements. These forward-looking statements are based upon Sunesis’ current expectations. Forward-looking statements involve risks and uncertainties. Sunesis’ actual results and the timing of events could differ materially from those anticipated in such forward-looking statements as a result of these risks and uncertainties, which include, without limitation, risks related to Sunesis’ need for substantial additional funding to complete the development and commercialization of vosaroxin, risks related to Sunesis’ ability to raise the capital that it believes to be accessible and is

required to fully finance the development and commercialization of vosaroxin, the risk that raising funds through lending arrangements may restrict our operations or produce other adverse results, the risk that Sunesis’ development activities for vosaroxin could be otherwise halted or significantly delayed for various reasons, the risk that Sunesis’ clinical studies for vosaroxin may not demonstrate safety or efficacy or lead to regulatory approval, the risk that data to date and trends may not be predictive of future data or results, the risk that Sunesis’ nonclinical studies and clinical studies may not satisfy the requirements of the FDA or other regulatory agencies, risks related to the conduct of Sunesis’ clinical trials, risks related to the manufacturing of vosaroxin and supply of the active pharmaceutical ingredients required for the conduct of the VALOR trial, the risk of third party opposition to granted patents related to vosaroxin, and the risk that Sunesis’ proprietary rights may not adequately protect vosaroxin. These and other risk factors are discussed under “Risk Factors” and elsewhere in Sunesis’ Quarterly Report on Form 10-Q for the quarter ended June 30, 2012, Sunesis’ Annual Report on Form 10-K for the year ended December 31, 2011 and Sunesis’ other filings with the Securities and Exchange Commission. Sunesis expressly disclaims any obligation or undertaking to release publicly any updates or revisions to any forward-looking statements contained herein to reflect any change in the company’s expectations with regard thereto or any change in events, conditions or circumstances on which any such statements are based.