Al-Maliki and al-Hashemi were seen arriving at Talabani's house, where the meeting was being held, in the Karrada district of Baghdad about 4:00pm (1300GMT) on Saturday.
The prime minister and al-Hashemi have a record of disagreement over many issues.
Al-Hashemi has complained that al-Maliki ignores his suggestions and even refuses to interact with him.
"This week may witness a significant step which may help in solving the problems," one Iraqi official said.
On Saturday, George Bush, the US president, said the Iraqi government still had "many important measures" to resolve in order to meet political goals.
"Unfortunately, political progress at the national level has not matched the pace of progress at the local level," Bush said.
"The Iraqi government in Baghdad has many important measures left to address, such as reforming the de-Baathification laws, organising provincial elections, and passing a law to formalise the sharing of oil revenues," he said.
|Al-Hashemi has complained that al-Maliki |
ignores his suggestions [AFP]
Al-Maliki has made a series of speeches in recent days in efforts to save his government and even travelled to Tikrit, the hometown of former Iraqi leader Saddam Hussein, where he tried to canvass support among Sunni tribal leaders.
But the absence of the Iraqi Islamic Party, the largest Sunni party will cast doubts on the credibility of Saturday's talks.
The Iraqi Islamic Party is the biggest party in the Accordance Front, the Sunni Arab bloc that pulled out of Maliki's cabinet last week in protest at his failure to address their demands for a greater say in government.
Hoda Abdel Hamid, Al Jazeera's Iraq correspondent, said it was hard to see what the talks could achieve without the main Sunni party.
She said that legally the remaining parties in the government could take decisions "but would it help the country, no? This is not an alliance that would bring about national reconciliation which is really the key to stopping the bloodshed".
Earlier on Saturday, al-Maliki and Talabani addressed a conference of Iraqi diplomats in Baghdad, stressing the need for friendly relations and support from all neighbouring countries.
The comments came amid accusations that the Shia-led government is biased toward Iran and against mainly Sunni Arab countries in the region, as well as threats of a Turkish incursion to face separatist Kurdish rebels in northern Iraq.
"Iraq has exerted and is still exerting great efforts to form the best relations with the Arab countries," Talabani said.
"We do not want to face the countries that are hostile to us, but we cannot sit silent forever. If things are not solved in a friendly way, Iraq is not as weak as they think."
Meanwhile, violence continued across Iraq.
About 16 mortar shells hit houses in the mainly Shia residential area of Sharqiya in Khalis, 80km north of Baghdad.
Three people were killed 24 wounded in the attack, according to local police.
In Kirkuk, broken glass and other debris were being swept from the bloodstained pavement, hours after a series of bombs struck commercial areas in the disputed city, killing at least four people and wounding 38.