Yemen is the poorest country in the Middle East and is on the verge of famine.
Qatar had accused the kingdom of politicizing the hajj, one of the pillars of Islam.
The four countries sanctioning Qatar are now asking it to agree with six "principles," rather than the original list of 13 demands.
The agreement is seen as a step toward ending the sanctions against the country.
The U.S. has sent mixed messaging on its stance.
Secretary of State Rex Tillerson called for Saudi Arabia to ease off Qatar, but President Donald Trump took a slightly different approach.