The government has instructed state schools to allow Syrian children to enrol for the new year starting in September even if their paperwork is not in order, government spokesman Mohamed Momani said.
"The children can get their situation sorted out during the school year," he told AFP.
"Carrying out this and other announced policy changes could help thousands more children attend school this semester," HRW said in a statement.
The education ministry has also set up double-shifts in 102 state schools, allowing 50,000 Syrian children to enrol, Momani said.
On Monday, the government also announced plans to create special classes for some 25,000 children aged 8 to 12 who had been deprived of schooling for the past three years or more.
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These will allow refugee children to catch up and have been funded in part by donations from the United States, Britain, Norway and Switzerland to the tune of around $100 million.
Bill Van Esveld, senior children's rights researcher at HRW, described the measures -- announced after the watchdog had urged Jordan to educate more Syrian children -- as "important".
"Jordan's education ministry has taken an important step by ordering schools to accept Syrian children this fall even if they don't have their papers in order," he said in the statement.
In a report issued on Tuesday, the New York-based watchdog said more than 80,000 school-aged Syrian children in Jordan had received no formal education in the past school year.
HRW said Syrian refugees in Jordan are required to have so-called interior ministry-issued "service cards" which are also needed for children to enrol in public schools.
Jordan says it currently hosts nearly 1.4 million refugees -- including 630,000 registered with the United Nations -- and has repeatedly called for more international help to cope.
"We have reached our limits... This is an international crisis and an international responsibility, and the world has to do its part," King Abdullah II said in statements published Monday.