WASHINGTON — The Obama administration began a full-press campaign on Sunday for Congressional approval of its plan to carry out a punitive strike against the Syrian government.

The lobbying blitz stretched from Capitol Hill, where the administration held its first classified briefing on Syria open to all lawmakers, to Cairo, where Secretary of State John Kerry reached Arab diplomats by phone in an attempt to rally international support for a firm response to the Aug. 21 chemical weapons attack in the suburbs of Damascus.

Mr. Kerry appeared on five morning talk shows, announcing new evidence — that the neurotoxin sarin had been used in the attack that killed more than 1,400 people — and expressing confidence that Congress would ultimately back the president’s plan for military action.

Behind closed doors on Capitol Hill, the administration presented classified intelligence to any senator or House member who wished to attend. About 80 did, but some from both parties emerged from the briefing convinced that the draft language authorizing military action would need to be tightened.