Mr Blinken met the Iraqi PM on the margins of United Nations General Assembly in New York, Secretary of State spokesman Matthew Miller said.
“The secretary conveyed an invitation from President Biden to the Prime Minister to visit the White House soon and reiterated the US commitment to assisting Iraq in achieving a secure, stable and sovereign future,” Mr Miller said.
Mr Al Sudani, who took office in October 2022, was the nominee of the Iran-aligned Co-ordination Framework, the largest political group in the Iraqi parliament with 138 out of 329 seats. The group comprises powerful Iran-backed Shiite militias and political parties.
Since then, Washington has grown increasingly worried over the influence of the Shiite militias. It has been pressing Iraq to introduce reforms mainly in economy, urging it to boost relations with its neighbours.
Iraq is caught in the middle of US-Iran rivalry and regional tensions, particularly due to its diplomatic and geographic closeness to Iran.
Last week, Assistant Treasury Secretary Elizabeth Rosenberg visited Iraq and met Mr Al Sudani and the Governor of the Central Bank of Iraq Ali Al Alaq.
They discussed bilateral relations and measures taken by the bank to fight money laundering and terrorist financing, the central bank said.
Washington has been pressing Iraq since last year to stop the flow of the dollar through the foreign currency auction run by the Central Bank of Iraq to countries under US sanctions, including Iran, Syria and Lebanon.
The Federal Reserve Bank of New York has applied strict measures on requests for international transactions from Iraq, rejecting many and delaying others.
It has also blacklisted several Iraqi banks suspected of money laundering and of carrying out suspicious transactions. The latest was in July when it barred 14 private Iraqi banks from conducting dollar transactions.
This has led to an increase in demand for the US dollar on the black market in Iraq, leaving the Iraqi dinar trembling against the dollar.
During the meeting in New York, Mr Al Sudani and Mr Blinken “renewed their commitment to continue strengthening the partnership between the two countries and reaffirmed the principles in the US-Iraq Strategic Framework Agreement,” Mr Miller said.
The agreement, which covers co-operation in different fields but mainly security, was signed as Washington began withdrawing most of its forces that had been stationed in Iraq since the 2003 US-led invasion in search of weapons of mass destruction that Saddam Hussein's regime was accused of developing and stockpiling. None were found.
American combat troops returned in force as part of a US-led international coalition to fight ISIS after the extremist militant group swept through large areas in northern and western Iraq in 2014.
Last week, Mr Al Sudani said his country was seeking a “new future relation” with the coalition, which still has about about 5,000 US troops in Iraq, as well as forces from other countries, to prevent a resurgence of ISIS after the group's defat in 2017.
"For sure, [the presence of] forces with the size of the International Coalition under that title and with that number of countries needs to be reviewed and that is what we agreed on during the visit to Washington," he said, referring to the first US-Iraq Joint Security Co-operation Dialogue held in August.
Mr Miller said Mr Blinken also "underscored US support" to Mr Al Sudani for the reopening of an oil pipeline between Iraq's northern semi-autonomous Kurdistan region and Turkey that has been shut since March.
Turkey said last week the pipeline, which contributes about 0.5 per cent of world oil supply, would be ready to resume operations soon, although it is unclear whether Baghdad and Ankara have agreed to the terms of a resumption of crude flows.
The statement added that Mr Blinken "commended the Prime Minister’s commitment to judicial independence in Iraq’s recent conviction and sentencing of multiple individuals on terrorism charges in connection with the killing of US citizen Stephen Troell."
Iraq last month sentenced an Iranian man and four Iraqis to life in prison over Troell's November 2022 killing in a middle class neighbourhood in central Baghdad.
Court officials did not name the defendants but said the four Iraqis were members of a Shiite militia.