Erdogan does not support the resignation and Soylu remains in office, the Communications Ministry said late on Sunday.
The interior minister stepped down Sunday after a chaotic take-off of the measure.
Solyu tweeted that he was taking full responsibility for the 48-hour curfew imposed on Friday in 31 cities.
The authorities came in for a lot of criticism for announcing the curfew only two hours before it entered into force on midnight on Friday.
Initially its deadline and details were unclear, leading to crowds in shops and widespread panic-buying with people defying the virus measures.
Only bakeries, pharmacies and some petrol stations are allowed to stay open during the curfew.
The opposition criticised the government for the sudden decision, which it said led to even further confusion.
Residents meanwhile adhered for the most part to the two-day partial lockdown.
Only a few citizens had violated the measure, the Interior Ministry said earlier on Sunday, according to state news agency Anadolu.
Turks in the 31 areas under lockdown, which include Istanbul and the capital, Ankara, are banned from leaving their homes from Friday midnight until midnight on Sunday.
Soylu had stressed in an interview published Sunday in the Hurriyet newspaper that the curfew was to end at midnight.
The lockdown covered nearly 64 million people in the country of 83 million, the ministry said.
Solyu had admitted in the interview that he had not foreseen the panic-buying, but added he did not believe the crowds on Friday evening posed a problem.
In his resignation tweet, Solyu said that he had been proud to serve as interior minister and would remain loyal to Erdogan.
He also asked him and the Turkish people for forgiveness.
The communications ministry, in stating that Solyu would continue in his post, underscored the minister’s merits.
It that Solyu had waged a determined fight against the outlawed Kurdistan Workers’ Party (PKK), locked in decades-long insurgency against the Turkish state.
Solyu, a member of Erdogan’s ruling AKP party has been interior minister since 2016.
Turkey’s coronavirus death toll jumped by 97 in a day to hit 1,198 on Sunday, Health Minister Fahrettin Koca said.
Confirmed cases rose to 56,956.
The weekend curfew is the strictest measure Turkey has taken so far.
Prior to it, people over 65, the chronically ill, and those under age 20 were banned from leaving their homes.
Schools, universities and public spaces are closed, as well as large events and mass prayers in mosques banned.
AFP
