On Monday, he told reporters: "I declare I am ready to resign my position as prime minister of the government ... so as to avoid the resignation of his excellency the president of the republic, Xanana Gusmao."
The premier said he had "deeply reflected" on the present situation in East Timor and said the interests of the nation were paramount.
"Assuming my own share of responsibility for the crisis affecting our country, I am determined not to contribute to any deepening of the crisis," he said, adding that he would stay on as a member of parliament.
"I am ready to dialogue with ... the president in order to contribute, if necessary, to the formation of an interim government," he said.
He said he hoped militants and his own party would accept his decision.
The statement was read out on the verandah of his official residence, in Portuguese, Tetun and English.
Alkatiri did not take any questions.