The International Cricket Council (ICC) chief executive vowed no compromise on safety after 19 were killed in the capital Islamabad.
"The ICC will not compromise the safety and security of any individual at one of its tournaments and if it is not appropriate to play in any country then we will not do so," Logart said in a statement.
Players from Australia, New Zealand and England have expressed concern over playing in Pakistan, which is due to hold the prestigious Champions Trophy from September 11-28.
Rawalpindi, one of three venues for the tournament, adjoins Islamabad where 14 policemen and five civilians were killed and scores injured in Sunday's attack.
Sri Lanka is the designated alternative venue but is also facing renewed violence between Tamil Tiger rebels and government troops, with South Africa mentioned as a possible replacement.
Lorgat said security was monitored during the Asia Cup while an ICC executive board meeting last week discussed an independent assessment. A security process had also been agreed ahead of the tournament, he said.
"Our consultants on security have been working with the Pakistan authorities during the Asia Cup and will report back to us as soon as possible with their views," he said.
A private security expert, hired by Australia, New Zealand and England has said there was work to be done ahead of the Champions Trophy.
"Some fine-tuning needs to be done and everyone acknowledges that," Reg Dickason said last week.
Pakistan Cricket Board chairman Nasim Ashraf, who attended the ICC meeting, said he was confident the biennial 'mini-World Cup' will be held in Pakistan.
Sri Lanka won the Asia Cup final in Karachi, beating India by 100 runs.