In a statement released on Tuesday, Abbas said: "This inciteful Israeli policy [of allowing Jewish extremists to visit the site] is a recipe for friction and violence."
The remark follows the detention of three Palestinians by Israeli police for preventing non-Muslims entering the site after Tel Aviv permitted visits several months ago.
For some Palestinians, the site is a symbol of an uprising for statehood. In September 2000, then Israeli opposition leader Ariel Sharon, now prime minister, visited the site in a storm of controversy.
The ensuing riot prompted the suspension of visits.
But Israel's rightist Public Security Minister, Tsahi Hanegbi, has promoted visits, saying Jews have a right to tour what may have been the site of destroyed Jewish temples. Israel took control of al-Haram al-Sharif in the 1967 Middle East war.
Israeli police said they would not allow non-Muslims to enter the mosques. "Any [non-Muslim] making any outward attempt to pray will be escorted out," national police spokesman Gil Kleiman told journalists.
Israel controls the site which contains Islam’s third most important mosque, posting police at entrances to maintain control although Muslims have formed a religious trust to administer al-Haram al-Sharif.
"This inciteful Israeli policy is a recipe for friction and violence"
Palestinian prime minister
Israeli police said three trust officials prayed at an entrance on Monday along with a dozen other Muslims, in such a way that non-Muslim visitors could not enter the site. Scuffles broke out and the officials were arrested on Tuesday, they said.
An Israeli judge freed two of them on bail of $1120 each and ordered them to stay away from the site for two months. The third was freed.
"We asked to distance them from the site for two months for incitement and their attempts to cause civil disorder," said Kleiman. "The case has been transferred to a prosecutor who will decide whether it is in the public interest to charge them."
Kleiman said the three were arrested so they could be questioned about the incident in which they were suspected of "incitement and attempting to cause a public disorder".
Adnan al-Husseini, who heads the Islamic religious trust, said the visits were "an unjust and illegal procedure" motivated by an Israeli desire to impose control over al-Aqsa mosque and that "extremist Jews" were among the visitors.
"[They] wanted to practise their religious rituals and this is rejected by all Muslims all over the world because this is an Islamic site," he said.