WASHINGTON—The White House is girding for more than a week of battle with Congress over President Barack Obama's plan to launch limited military strikes against the Syrian regime for its alleged use of chemical weapons last month.

To back the administration's position, Secretary of State John Kerry said Sunday that the U.S. had obtained new blood and hair samples from inside Syria that confirmed President Bashar al-Assad's regime used sarin, a powerful nerve agent, against civilians in an Aug. 21 attack on an eastern Damascus suburb.

Mr. Kerry said he believed this new evidence will help the White House build more support on Capitol Hill and among allies in Europe and the Middle East to take military action aimed at degrading Mr. Assad's ability to conduct chemical warfare.

The leaders of the House and Senate said they would hold votes on the need for military action in Syria during the week of Sept. 9.

The administration quickly began making its pitch to lawmakers. On Sunday, it held a classified briefing on Capitol Hill, and on Monday, Sens. John McCain (R., Ariz.) and Lindsey Graham (R., S.C.) were invited to the White House for a special briefing. The two, who have pressed for a more forceful strike on Syria than the cruise missile attack telegraphed by the administration, are expected to be key players as Mr. Obama tries to gather support for military action.