Bahrain, Egypt, Saudi Arabia and the United Arab Emirates said in a joint statement they would respond "in a timely manner”.
The countries did not elaborate on what steps they could take, though a major credit rating agency warned it had changed Qatar’s economic outlook to negative over the turmoil.
The countries cut ties to the Fifa 2022 World Cup host early last month over its alleged support for extremist groups and ties with Iran.
Qatar denies supporting extremists and has defended its warm relations with Iran. The two countries share a massive undersea natural gas field.
The four nations issued a 13-point list of demands on June 22, giving Qatar 10 days to comply.
They later extended the deadline by another 48 hours at the request of Kuwait, which has acted as a mediator to resolve the crisis. That deadline expired early on Wednesday morning.
Later on Wednesday, foreign ministers from the four Arab countries will meet in Cairo to discuss their next move.
On Tuesday, Egypt’s state-run MENA news agency reported intelligence agency chiefs from those countries had met in Cairo, probably discussing the crisis.
What Qatar said in response to the demands remains unclear.
It has called the demands, which include shutting down its Al-Jazeera satellite news network, expelling Turkish military forces based in the country and paying restitution, an affront to its sovereignty.
The crisis has become a global concern as neither side appears to be backing down. Qatar, the world’s biggest exporter of liquefied natural gas, hosts some 10,000 American troops at its sprawling al-Udeid Air Base.
US secretary of state Rex Tillerson has been trying to ease tensions, while President Donald Trump’s comments on Qatar funding extremist groups back the Saudi-led countries’ position.
The nations could impose financial sanctions or force Qatar out of the Gulf Co-operation Council, a regional body known as the GCC that serves as a counterbalance to Iran.
Emirati foreign minister Abdullah bin Zayed Al Nahyan kept up the pressure on Qatar, saying: "To defeat terrorism, we must confront extremism, we must confront hate speech, we must confront the harbouring and sheltering of extremists and terrorists, and funding them.
"Unfortunately, we in this region see that our sister nation of Qatar has allowed and harboured and encouraged all of this.”
He added: "Enough is enough.”
Qatar’s foreign minister meanwhile criticised the four Arab nations for trying to isolate his country "under the banner of fighting terrorism”.
Sheikh Mohammed bin Abdulrahman Al Thani said: "When measures clothed in this context, it is because they think they will be met with international sympathy because they are ’anti-terrorism’ measures.”
The credit ratings agency Moody’s warned early on Wednesday that it had set Qatar’s economic outlook to negative over the crisis.
"Public exchanges between the various parties in recent weeks and previous periods of heightened tensions between Qatar and other GCC countries suggest that a quick resolution is unlikely and that the stalemate may continue for some time,” Moody’s said.