McCain made the remarks to reporters in Baghdad, where he and five other members of Congress were meeting with U.S. and Iraqi officials.
"The American people are disappointed and frustrated with the Iraq war, but they want us to succeed if there's any way to do that," McCain, a possible 2008 presidential candidate, said at a news conference at the U.S. Embassy in Baghdad's heavily fortified Green Zone.
The Arizona Republican said five to 10 more brigades of U.S. combat soldiers must be sent to Iraq. Brigades vary in size but generally include about 3,000 troops, meaning he was recommending 15,000 to 30,000 additional forces.
Sen. Joseph Lieberman, D-Conn., said the delegation had met with Prime Minister Nouri al-Maliki, a Shiite, and urged him to break his ties with anti-U.S. cleric Muqtada al-Sadr and disarm his Mahdi Army militia.
Al-Sadr controls 30 of the 275 parliament seats and is a key figure in al-Maliki's coalition.
The U.S. military has about 140,000 troops in Iraq, and President Bush is considering a change of strategy in the country, including Baghdad, where stepped-up efforts to curtail sectarian violence failed this summer. The U.S. force includes about 15 combat brigades made up of 50,000-60,000 soldiers, the U.S. military said.
McCain has joined other legislators and military analysts in saying that Mr. Bush sent far too few troops to Iraq after the coalition toppled Saddam Hussein in March 2003, leading to widespread violence at the hands of Sunni Arab insurgent groups and Shiite militias.
But McCain said U.S. military commanders in Iraq had not asked the delegation for more U.S. troops, and one of the senators traveling with him didn't seem to accept his argument.
"Iraq is in crisis. The rising sectarian violence threatens the very existence of Iraq as a nation," said Sen. Susan Collins, R-Maine. The current U.S. strategy in Iraq has failed, but "I'm not yet convinced that additional troops will pave the way to a peaceful Iraq in a lasting sense," she said.
"My fear is that if we have more troops sent to Iraq that we will just see more injuries and deaths, that we might have a short-term impact, but without a long-term political settlement," Collins said.
Gunmen in military uniforms kidnapped dozens of people Thursday from a commercial area in central Baghdad, police said, and a car bomb killed two policemen who were trying to defuse it in Baghdad's Sadr City section, where officers were on high alert after receiving tips that militants were moving more bombs into the Shiite slum.
McCain said he realizes that only about 15 percent to 18 percent of Americans favor deploying more U.S. troops to Iraq, and that if such a move proved unsuccessful in the unpopular war it could hurt his presidential ambitions.
But the Vietnam War veteran also said that Americans must realize that if U.S. troops leave Iraq in a state of chaos, insurgent groups such as al Qaeda in Iraq "will follow us home."
Lieberman said the U.S. delegation left its meetings with al-Maliki, President Jalal Talabani and other Iraqi officials believing "there is a force of moderates within the context of Iraqi politics coming together to strengthen the center here against the extremists."
"We need more, not less, U.S. troops here" to improve Iraq's security, he said.
Lieberman said the U.S. delegation was "quite explicit" about "how important it is that the Iraqis themselves begin to take aggressive action to disarm the militias, to stop the sectarian violence and to involve all the people in country to governance," including promised provincial elections.
Last month, Lieberman won re-election to the U.S. Senate as an independent after losing the Democratic primary in his state of Connecticut in part because he supports the Iraq war.
The delegation also included Republican Sens. Lindsey Graham of South Carolina and John Thune of South Dakota, and Rep. Mark Kirk, R-Ill.
They were scheduled to travel on Thursday to Iraq's southern port city of Basra and to Ramadi, the capital of Anbar province, a dangerous area where many insurgent groups are fighting U.S. and Iraqi forces.