WASHINGTON, Dec. 14  The White House said Thursday that a Democratic senator’s meeting with President Bashar al-Assad of Syria was inappropriate and undermined democracy in the region, while three more senators, including a Republican, made plans to visit Damascus in defiance of President Bush.

The visits are troublesome for the Bush administration because they come in the wake of the report by the bipartisan Iraq Study Group, which has called for the United States to engage in direct talks with Iran and Syria. Mr. Bush has steadfastly resisted such talks, and the visits by the senators could add to public pressure on the White House to change that policy.

Senator Bill Nelson, Democrat of Florida, was in Damascus on Wednesday to meet with Mr. Assad; he later told reporters that he saw a “crack in the door” for the United States to cooperate with Syria on Iraq. Senators Christopher J. Dodd, Democrat of Connecticut; John Kerry, Democrat of Massachusetts; and Arlen Specter, Republican of Pennsylvania, all plan to visit Syria in the coming weeks.

All have been discouraged by the Bush administration from going, though Mr. Nelson and Mr. Kerry, who were traveling separately in the Middle East on Thursday, said in interviews that they had visited Syria before without any complaint from the White House.