Iraqi Prime Minister Nouri Maliki has urged the Kurdish authorities in northern Iraq to hand over fugitive Vice-President Tariq al-Hashemi.
An arrest warrant was issued for Iraq's most senior Sunni Arab politician on Monday on terrorism charges.
Mr Hashemi denies the charges and his entire political bloc is boycotting parliament and the cabinet.
Tensions between Sunnis and the Shia Arab majority appear to be coming to a head, a BBC correspondent says.
Mr Hashemi is currently in Irbil, under the protection of the Kurdistan regional government. The warrant was issued a day after US troops pulled out of Iraq.
US Vice-President Joe Biden has urged Iraqi leaders to work together to avert renewed sectarian strife.
Mr Maliki, a Shia Arab, said on live TV that he would dismiss ministers belonging to Mr Hashemi's bloc, al-Iraqiyya, if they did not lift their boycott.
He invited all political factions to hold talks to try to resolve the crisis.
Otherwise, he said, Iraq could in future have a majority government which any person or bloc would be welcome to join to "take the country forward in a positive direction".
In a statement quoted by Reuters news agency, al-Iraqiyya rejected the invitation to talks, saying Mr Maliki himself was "the main reason for the crisis and the problem".
Asked about Mr Hashemi's call for the Arab League to oversee any investigation into the allegations, Mr Maliki said this was a criminal issue in Iraq.
He saw no reason why the Arab League or the UN should intervene in an Iraqi criminal case, he said.
"We do not accept any interference in Iraqi justice," he added. "We gave Saddam a fair trial, and we will give Hashemi a fair trial too."
Mr Hashemi denies allegations that he funded attacks on government and security officials during Iraq's bloody insurgency.
On Monday evening, Iraqi television showed purported confessions from his bodyguards, but the vice-president says that they were false and "politicised".
He told reporters in Irbil on Tuesday: "I swear to God that I never committed a sin when it comes to Iraqi blood."
He said he would be willing to face trial in Kurdistan.
Mr Maliki went on TV after speaking on the phone to Mr Biden.
The US vice-president "stressed the urgent need for the prime minister and the leaders of the other major blocs to meet and work through their differences together", the White House said.
Mr Maliki leads a government of national unity in a fragile power-sharing deal that has lasted a year.
Iraq has a majority Shia population, but the areas adjacent to the Syrian border are almost entirely Sunni-dominated.
BBC Middle East correspondent Jim Muir says Sunni-majority provinces which had previously shown little interest in setting up Kurdistan-style autonomous areas have begun to embrace that idea.
This worries the prime minister, who fears an alliance between Sunni areas of Iraq and a possible future Sunni-controlled Syria, should the government of Bashar al-Assad fall, our correspondent adds.