Exhibit 99.1

Investor Contact:   Sunesis Pharmaceuticals, Inc. Eric Bjerkholt 650-266-3717 Media Contact:   Sunesis Pharmaceuticals, Inc. Dan Weinseimer 650-266-3739

Sunesis Pharmaceuticals Receives NASDAQ Notification

SOUTH SAN FRANCISCO, Calif., (September 18, 2009) – Sunesis Pharmaceuticals, Inc. (NASDAQ: SNSS) reported today that it received a letter, dated September 16, 2009, from the Listing Qualifications Staff (the “Staff”) of The NASDAQ Stock Market notifying Sunesis that it does not comply with the minimum $1.00 per share requirement for continued listing on The NASDAQ Capital Market set forth in NASDAQ Listing Rule 5550(a)(2). The notice further provides that, pursuant to Listing Rule 5810(c)(3)(A), if, at any time before March 15, 2010, the bid price for Sunesis’ common stock closes at $1.00 or more for the minimum 10 consecutive business days required, the Staff will provide written confirmation to Sunesis that it complies with Listing Rule 5550(a)(2), unless the Staff exercises its discretion to extend this 10 day period pursuant to Listing Rule 5810(c)(3)(F).

The NASDAQ notice does not impact Sunesis’ listing on The NASDAQ Capital Market at this time and Sunesis will continue to trade under the symbol “SNSS.”

If Sunesis does not demonstrate compliance with Listing Rule 5550(a)(2) by March 15, 2010, the Staff will determine whether Sunesis meets The NASDAQ Capital Market initial listing criteria set forth in Listing Rule 5505, except for the $1.00 per share bid price requirement. If Sunesis meets the initial listing criteria, the Staff will notify Sunesis that it has been granted an additional 180 calendar day compliance period. If Sunesis is not eligible for an additional compliance period, the Staff will notify Sunesis that its common stock will be delisted. At that time, Sunesis may appeal to the NASDAQ Listing Qualifications Panel (“Panel”), and Sunesis would remain listed pending the Panel’s decision. Sunesis cannot provide any assurance that the Panel will allow Sunesis to remain listed in the event of any appeal.

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, voreloxin, in multiple indications to improve the lives of people with cancer. For additional information on Sunesis Pharmaceuticals, please visit http://www.sunesis.com.

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

This press release contains forward-looking statements, including without limitation statements related to the continued listing of Sunesis’ common stock on The NASDAQ Capital Market and potential outcomes in the event of Sunesis’ continued non-compliance with the NASDAQ listing standards. Words such as “may,” “will” 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 associated with Sunesis’ failure to comply with the continued listing requirements of The NASDAQ Capital Market and the risk that Sunesis becomes subject to delisting proceedings by NASDAQ. 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, 2009 and 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.