Without naming any US officials, al-Maliki said some of the criticism of him and his government had been "discourteous".
He said: "No one has the right to place timetables on the Iraq government. It was elected by its people.
"Those who make such statements are bothered by our visit to Syria. We will pay no attention. We care for our people and our constitution and can find friends elsewhere."
Toppling al-Maliki would require a majority vote in the 275-member Iraqi parliament.
As long as the Kurdish parties and the main Shia bloc stand beside him, his opponents lack the votes, despite some recent defections by smaller parties.
Much of the Shia and Kurdish support for al-Maliki is based on fear of what might happen if he were to go.
Under the constitution, the entire cabinet would have to be dissolved, and all ministries would be up for grabs.
Deciding who would get the nearly 40 cabinet-level posts could take months, paralysing the government.
As US support for al-Maliki ebbed further on Tuesday, Ryan Crocker, the US ambassador to Iraq, described Iraq's political progress "extremely disappointing".
Bush, at a summit in Canada, said that the Iraqi people, not their government, deserved credit for reconciliation efforts.
"If the government doesn't respond to the demands of the people, they will replace the government."
"That's up to the Iraqis to make that decision, not American politicians," he said.
Bush acknowledged it was difficult for Iraq to make the transition to democracy, but did not repeat his past assertions of confidence in Iraq's struggling prime minister.
"There's a certain level of frustration with the leadership in general," Bush said.
On Monday, senators Carl Levin, the chairman of the Senate Armed Services Committee, and John Warner, the panel's top Republican, said they were not optimistic about the political situation in Iraq.
|"It's not just the issue of the prime minister, it's the whole government that has to perform here|
Ryan Crocker, US ambassador to Iraq
"We believe that the recent high-level meetings among Iraqi political leaders could be the last chance for this government to solve the Iraqi political crisis," they said in a joint statement following a visit to Iraq.
Iraqi leaders had "failed to meet their own political benchmarks on sharing power and resources, changing de-Baathification laws, scheduling provincial elections, or amending the constitution," Levin said.
"So I hope that the Iraqi assembly, when it reconvenes in a few weeks, will vote the Maliki government out of office and will have the wisdom to replace it with a less sectarian and a more unifying prime minister and government," he said.
Bush insisted that the US troop surge in Iraq had made it possible for what he described as a "bottom-up" political reconciliation driven by Iraq's people, not its political leaders.
Crocker and General David Petraeus, the most senior US commander in Iraq, are to report to the US Congress by mid-September on their efforts to halt sectarian violence and return Iraq to viable self-governance.
"It's not just the issue of the prime minister, it's the whole government that has to perform here," Crocker said.
He added that Washington expected a "serious effort to achieve national reconciliation."
Maliki has called a reconciliation summit in an attempt to rescue his crumbling national unity government.
However, it has been boycotted by key political blocs, including the main Sunni group the National Concord Front.