Two high-ranking US senators are demanding that Washington deploy some 20,000 troops to Syria and Iraq.

Republicans John McCain and Lindsey Graham called on Sunday for Washington to nearly triple the US military force levels in Iraq to 10,000, and send an equal number of troops to Syria to ‘counter’ Daesh (ISIL) terrorists in both countries.

McCain and Graham also criticized President Barack Obama's Daesh strategy, which relies on airstrikes and modest support to what Washington deems as ‘moderate’ militants in Syria, stressing the need for greater US in the Middle East conflicts.

"The only way you can destroy the caliphate (Daesh) is with a ground component," said Graham who is seeking his party's presidential nomination. "The aerial campaign is not turning the tide of battle," Reuters reported.

McCain, chairman of the Senate Armed Services Committee, recently proposed intervention in Syria by a European and Arab ground force backed by 10,000 US military advisers and trainers.

On Sunday, both senators told reporters during a visit to Baghdad, the Iraqi capital, that US personnel could provide logistical and intelligence support to a proposed 100,000-strong force from countries like Egypt, Turkey and Saudi Arabia.

Last month, the US president ordered the deployment of dozens of special operations troops to northern Syria to “advise” what it calls ‘opposition forces’ in their fight against ISIL.

US counter-terrorism experts have warned that deploying ground troops risks backfiring.

The so-called US-led coalition, which has been bombing purported militant targets in Syria and Iraq for more than a year now, relies heavily on American resources despite including some 60 nations, according to Reuters.

The senators met earlier with Iraqi Prime Minister Haider al-Abadi who they said had welcomed the idea of more US troops.

However, Iraqi government spokesman Saad Hadithi denied the claim, saying that the PM had not requested US combat troops on the ground but rather asked for more arms and advisers to increase air support for Iraqi forces.

Leading Iraqi politicians have repeatedly voiced opposition to a greater role for US forces, which withdrew in 2011 after a nearly nine-year war that left huge casualties.