The decision by Mahmoud Abbas on Wednesday night highlights tensions with Hamas in the wake of the Islamist group's victory over the president's long-dominant Fatah in elections in January.
Officials close to Abbas, also known as Abu Mazen, said he had come under pressure from the European Union, which threatened to withdraw its monitors from the key Rafah crossing between Gaza and Egypt in response to Hamas's rise to power.
But Ismail Haniyeh, the prime minister, said on Thursday: "The government does not accept the creation of parallel bodies that may take away its authority.
"This is an elected government, not an appointed one. Brother Abu Mazen confirmed to me more than once that he will not touch the authority of the current government."
He said that he would meet Abbas later on Thurdsay to discuss the crossings and other security concerns.
Abbas's office issued a presidential decree late on Wednesday taking over the Gaza crossings.
Analysts said that this could spark a political crisis, something some see as inevitable because of the conflicting political agendas of the two sides.
Hamas is sworn to Israel's destruction, while Abbas and Fatah want a negotiated two-state agreement to end conflict.
Talal Awkal, a Palestinian political analyst, said: "There is a fear we may have two governments, justified by the challenge that whenever Israel threatens to block something we transfer it into the president's authority."
A security official said that Abbas named Rashid Abu Shbak, currently head of the powerful Fatah-dominated Preventive Security Service, as chief of internal security.
In his new post, Abu Shbak would be in charge of Preventive Security, police and the civil emergency services.
The interior minister, Saeed Seyam of Hamas, has authority over the three security services. Although Abu Shbak would be answerable to Seyam, only Abbas would be able to dismiss him, the official said.
Haniyeh said he would discuss with Abbas disputes over who is responsible for the security forces. The outgoing interior minister, from Fatah, said last week that Seyam had no authority over larger security agencies.