KUALA LUMPUR (Reuters) - Malaysian Prime Minister Najib Razak on Friday sacked his former deputy from the ruling party and said he needed more time to think about a cabinet reshuffle.

Former deputy prime minister Muhyiddin Yassin was sacked from the United Malay National Organisation (UMNO), along with Mukhriz Mahathir, the son of former prime minister Mahathir Mohamad.

Both have been tough critics of Najib, calling for his resignation following allegations of graft and mismanagement at scandal-hit state fund 1Malaysia Development Berhad.

Najib, who chaired the advisory board of 1MDB, has faced intense pressure following revelations that up to $1 billion had been deposited into his personal account. Najib has denied any wrongdoing.

He also said he needed more time to think about a cabinet reshuffle. He announced his plan to rejig the lineup after the ruling coalition won the Sarawak state elections by an increased majority last month.

"I need more time to think about it," he told reporters.

The last cabinet reshuffle was last July, when Najib culled leaders critical of his handling of 1MDB.

Malaysia's ruling coalition, Barisan Nasional, coasted to victory in two by-elections earlier this month, defying a political movement led by Mahathir who has sought to turn voters against Najib.

The wins, along with a landslide win in the Borneo state of Sarawak last month, prompted some political experts to believe Najib may call snap polls.

Najib dismissed these rumors.

"(National) polls are not governed by by-elections. National polls are governed by various other factors," he said.

(Reporting by Joseph Sipalan; Editing by Clarence Fernandez and Nick Macfie)