The Turkish president met people affected by the earthquakes on Wednesday
At least 15,000 people are confirmed dead in Turkey and northern Syria.
Critics claimed the emergency services' response was too slow and the government was poorly prepared.
Mr Erdogan accepted the government had encountered some problems, but said the situation was now "under control".
The leader of Turkey's main opposition party, Kemal Kilicdaroglu disagreed.
"If there is one person responsible for this, it is Erdogan," he said.
The president rejected the accusation and said unity was required in the aftermath of the disaster, "In a period like this, I cannot stomach people conducting negative campaigns for political interest," he told reporters in Hatay.
Thousands of survivors have been spending a third night in freezing conditions, with hope fading for many trapped under the rubble.
A World Health Organization official has warned there could be significant injuries caused by freezing temperatures among survivors of the quakes.
"We've got a lot of people who have survived now out in the open, in worsening and horrific conditions," said WHO earthquake response incident manager Robert Holden on Wednesday.
"We are in real danger of seeing a secondary disaster which may cause harm to more people than the initial disaster if we don't move with the same pace and intensity as we are doing on the search and rescue."
In nearby Syria, relief efforts have been complicated by years of conflict that has destroyed the nation's infrastructure.
The Bab al-Hawa crossing between Turkey and Syria has been closed since the earthquake as the roads were badly damaged.
While a senior UN official said the road may soon be accessible, Turkey's Foreign Minister Mevlut Cavusoglu confirmed the country was working to open two more border gates to help get aid into the country.
"There are some difficulties in terms of Turkey's and the international community's aid [reaching Syria]. For this reason, efforts are being made to open two more border gates," he said.
People receive food at a shelter
The EU has confirmed it will send €3.5m (£3.1m) in aid to Syria following a government request for assistance, but said the aid must be delivered to both government- and rebel-controlled areas.
More than 1,500 people have died in Idlib province alone and an adviser to Syrian President Bashar al-Assad said sanctions were stopping Syria from receiving the aid it needed.
"We don't have enough bulldozers, we do not have enough cranes, we do not have enough oil due to European and American sanctions," Bouthaina Shabban said.
--- Courtesy of BBC Sport