Monday’s blast at the 21,000-seat Manchester Arena took place shortly before 10.35 p.m. (21.35 GMT) local time.
Police said 22 people died and 59 were injured. One man is thought to have detonated an explosive device, but died at the scene.
The arena had been hosting a concert by U.S. pop star Ariana Grande; thousands of children and young teenagers were among the crowd.
President Recep Tayyip Erdogan said he "strongly condemned" the attack during a speech at Istanbul University.
"We share the grief of the British government and its people," Erdogan said. "Like every country, I would like to stress that we stand with Britain in the fight against terrorism."
Prime Minister Binali Yildirim also condemned the attack during a news conference in Georgia alongside his counterpart Giorgi Kvirikashvili.
"We offer our condolences to our ally the United Kingdom, the victims' families and we wish a speedy recovery to the injured.
“We condemn this attack in the strongest possible words," Yildirim said.
"We know what terrorism can do, we paid a big price because of it. Terror is a global threat and should be dealt with globally," he added.
Foreign Minister Mevlut Cavusoglu tweeted earlier on Tuesday: "I condemn the terrorist attack in Manchester. Sincere condolences to the British Government and... people."
The Foreign Ministry said it offered “sincere condolences to the people of the United Kingdom” describing it as a country “which knows and feels the brutality of these inhumane and cowardly attacks".
It added: "We will continue our dedicated and efficient fight against terrorism, to eradicate this menace with our ally the United Kingdom.
“This will be the best answer to the cowardly attack in Manchester."
Turkey's EU Affairs Minister Omer Celik has also used Twitter to share his thoughts on the attack
"The ones who massacre innocent people are enemies of humanity. They attack on all humanity." Celik said. "Terror has no religion, language, race or country. Our joint fight against this scourge will continue unabated at all fronts."