Straw described the 20-minute meeting on the sidelines of an international conference on Iraq held in this Egyptian Red Sea resort as "very good".
"What we all look forward to is for this matter to be resolved within the IAEA (International Atomic Energy Agency) board," he told journalists.
The Islamic republic announced Monday it had suspended its uranium enrichment activities in a bid to ease international fears over its suspected nuclear weapons programs and to avoid possible sanctions.
The decision came after negotiations with the three big EU powers, Britain, France and Germany.
Kharazi, standing at Straw's side, said "we are very glad we have reached this conclusion."
He dismissed worries Iran wanted to build a nuclear arsenal, saying "we are for the peaceful use of nuclear power, which is our right."
The IAEA, the UN nuclear watchdog, is to hear a report Thursday on Iran's compliance.