On Sunday, the states boycotting Qatar agreed to a Kuwaiti request to extend by 48 hours Sunday's deadline.
German Foreign Minister Sigmar Gabriel, who on Monday starts a tour of several Arab states, called for a "serious dialogue" to end the crisis.
They have not specified what further sanctions they could impose on Doha but commercial bankers in the region believe that Saudi, Emirati and Bahraini banks might pull deposits and interbank loans from Qatar.
Chris Doyle, Director of the Council for Arab-British Understanding, told Sky News: "It's an extraordinary list of demands, because essentially it would mean that Qatar would become a vassal state of Saudi Arabia".
The response will be the focus of a meeting in Cairo on Wednesday of foreign ministers from the four countries that have cut ties with Qatar.
Earlier, as the original deadline expired, Saudi-owned television Al Arabiya reported that Qatar could be hit by further sanctions.
Arab countries said that there is no scope for agreement on demand and at the same time it warned that if Qatar does not accept these demands then steps will be taken against it. The United Arab Emirates has threatened Qatar with "divorce" from its Gulf neighbors if it failed to meet the demands, saying they were non-negotiable.
However, Qatari foreign minister Sheikh Mohammed bin Abdulrahman Al Thani said the 13-point ultimatum was "made to be rejected".
The requests include the severance of Qatar's relations with Iran, closure of Turkey's military base on Qatar's territory and a shutdown of the Al Jazeera TV channel.
"He reiterated the importance of stopping terrorist financing and discrediting extremist ideology", according to the White House.
While Trump has largely echoed the concerns of the blockading nations, his secretary of state, Rex Tillerson, has called for an end to the blockade, which he said has hurt USA interests in the region.