Testifying before the Senate Foreign Relations Committee, Baker said, "We could get them (Syria) to get Hamas to recognize Israel's right to exist. It would be a huge step in the right direction."
Hamas, which is designated a terrorist organization by the State Department and the European Union, dominates the Palestinian government through its election a year ago.
The Bush administration has been reluctant to talk to Syria, citing its support for groups like Hamas. Baker was secretary of State under Bush's father, the first President Bush.
Baker told the committee he had discussed the situation with senior Syrian officials on a trip to the country as co-chair of the Iraq Study Group, a bipartisan panel that recommended several changes in Bush's Iraq strategy. Most of the recommendations were ignored by the administration.
'Syria sending signals'Baker said the United States in talks with Syria also "could get them to stop arming Hizbullah," a Lebanese terror organization backed by Iran that has a foothold in the Lebanese government and fought a war with Israel last summer.
The co-chair of the study group, former Rep. Lee Hamilton, D-Ind., said Syria has been "sending signals to us" that they want to talk to the United States.
The study group recommended the Bush administration hold talks with Iran as well as Syria and other countries in the region as part of a diplomatic effort to end the fighting in Iraq.
Sen. Bill Nelson (news, bio, voting record), D-Fla., who held talks in Syria in December with President Bashar Assad and Foreign Minister Walid al-Moualem, said, "The administration has adopted the approach of an ostrich."
"And make no mistake. It is not working," he told the private Council on Foreign Relations.
Nelson said Assad had "indicated an interest" in discussing its border with Iraq. Nelson said jihadists make their way into Iraq to fight US troops.