Two British soldiers were seriously injured by a missile fired by the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) armed group in eastern Syria on Saturday, according to a war monitor.

The Syrian Observatory for Human Rights said the pair were part of the international anti-ISIL coalition, led by the United States.

"The two British soldiers were transported by helicopter to receive medical care," Rami Abdulrahman, the Observatory's director, told AFP news agency.

A Kurdish fighter from the Syrian Democratic Forces (SDF) died in the attack in the village of Al-Shaafa in Deir Az Zor province, one of the last pockets of territory still controlled by ISIL in the Euphrates River valley.

The SDF, a coalition dominated by Kurdish fighters, has spearheaded the fight against ISIL, supported by several Western countries, including the United Kingdom.

The international alliance seized the key ISIL holdout of Hajin in December after months of fighting that has seen the group launch vicious counterattacks.

ISIL, which once controlled swaths of Syria and Iraq, has been pounded by multiple offensives.

Since September, more than 1,000 ISIL members have been killed in the fighting compared with just under 600 SDF members while 15,000 people have fled Hajin, according to the Observatory.

Last month US President Donald Trump announced the withdrawal of about 2,000 soldiers from Syria, deployed to support the SDF, claiming ISIL had been defeated. US officials, however, have not delivered a timeline for the pullout.

The Syrian war, which began in 2011, has caused more than 370,000 deaths and forced millions of people to flee their homes.