Majority Leader Eric Cantor, R-Va., also said at a news conference he hopes the street protests taking place in Cairo and elsewhere will lead to a democratic society that "stands for human rights, progress and equal opportunity."
In his remarks, Cantor did not criticize President Barack Obama over his handling of the two-week crisis.
GOP leaders have privately urged members of the rank and file not to second-guess Obama's approach to the crisis, in which hundreds of thousands of Egyptians have staged demonstrations demanding that President Hosni Mubarak surrender power.
Asked about criticism leveled recently by another Republican lawmaker, Cantor said, it would not be "helpful for this President, who is having a tough enough time as it is, to have 535 members of Congress to opine on his conduct of foreign policy."
Yet with his remarks, which aides said were planned in advance, Cantor appeared to be articulating a different policy objective than the one Obama has spoken of most frequently.
"I think the primary goal should be to stop the spread of radical Islam. That is where our focus should be," he said.
Since the protests first arose, Obama has called for a transition to a government - regardless of its leader - that grants greater freedoms than Mubarak allows in a nation of 80 million.
"The future of Egypt will be determined by its people. It's also clear that there needs to be a transition process that begins now. That transition must initiate a process that respects the universal rights of the Egyptian people and that leads to free and fair elections," the president said late last week.
Mubarak, who has been in power nearly 30 years, has been a strong ally of the United States in the Middle East as well as in its attempt to rein in international terrorists. He also has abided by the peace treaty with Israel signed by his predecessor.
At the same time, in recent years U.S. presidents have urged Mubarak to allow greater freedoms for Egyptians, including free elections.
Cantor is Jewish and a strong supporter of Israel, whose leaders have been watching events unfold in Egypt with apprehension.
Asked whether Cantor's remarks stemmed at least in part from his position on Israel, Cantor spokesman Brad Dayspring said the majority leader "has consistently made clear that the expansion of radical Islam is a global danger and is bad for America and our allies."
Other traditional congressional supporters of Israel have also remained on the sidelines while Obama grapples with the protests in Egypt.
Simultaneously, one of the most powerful lobbying organizations in Washington, the American Israel Public Affairs Committee, has been largely silent on the fast-moving developments. AIPAC holds considerable sway with lawmakers and many take their lead from the group.
Associated Press writer Donna Cassata contributed to this report.