The move came after a series of high-level meetings between the Turkish government and executives from the company last week, and after Ankara provoked a storm in March by trying to ban the network in the country entirely.
The accounts blocked on Sunday had published a series of leaks ahead of the municipal elections on March 30, including phone conversations which appeared to link the government and the prime minister to a vast corruption scandal.
Users reported that the two accounts were reported as "withheld" when they tried to access them from within the country over the weekend.
Twitter's global policy team said it withholds content only "after due process", such as after having received a court order, and in a tweet said it would not do so "at the mere request of a gov't official".
It added that it would not give details of the two accounts' users to the government.
"Twitter has not provided and will not provide user information to Turkish authorities without valid legal process," it said.
The government, which accuses those behind the accounts of publishing false and harmful content, is also pressing the company to hand over details on the owners of a dozen other accounts.
Erdogan has asked Twitter -- which has 10 million users in Turkey -- to open a liason office in the country, and has criticised the microblogging site for not paying taxes there.
Twitter has ruled out any such move, refusing to open an office in a state that tried to ban the site, and has rejected charges of tax evasion. It said its advertising sales in Turkey are handled through a reseller that pays applicable levies.
Erdogan's government had to unblock Twitter on April 3 after the country's top court ruled that the ban breached constitutional guarantees on free speech.
The video-sharing site YouTube has been blocked in Turkey since the end of March despite two separate court orders calling on the ban to be lifted, after an audio recording allegedly showing top civilian and military officials during high-level security talks on Syria was posted on the site.