Suleiman held talks on Wednesday with Israeli Foreign Minister Silvan Shalom in Jerusalem.
After the meeting, Shalom said he had reviewed with Suleiman all the issues that would pave the way for implementing Israel's Gaza disengagement plan.
Suleiman, who also met Israeli State Minister Benyamin Ben Aleazer, expressed his belief that the disengagement will happen peacefully.
The Palestinians are demanding that Israeli troops pull out of the buffer zone along with the rest of the occupied Gaza Strip this summer.
But Israel wants the two redeployments treated separately and is determined to retain the right to re-enter the border strip if Egyptian troops prove unable to stop arms smuggling across the border by Palestinian resistance fighters.
"The Israeli withdrawal [from Gaza] is in no way related to the agreement with Egypt on the Philadelphi road," Israeli ambassador to Egypt Shalom Cohen said ahead of the visit.
The planned Israeli pullout from
Gaza is on Suleiman's agenda
"There is the issue of reversibility," he said, stressing that, while the Gaza pullout was a definitive policy shift, any redeployment from the border strip would be provisional.
Cohen said there were also differences over the size of the Egyptian force to take over patrols in the strip, with negotiations currently focussing on a 750-strong contingent to man the 15-km long corridor.
The ambassador stressed that the Gaza withdrawal would go ahead even without agreement with the Egyptians on the border issue.
"Israel will withdraw from the Gaza Strip and keep a military presence on the Philadelphi road until we are sure that smuggling has stopped."
But he expressed confidence that a deal could be struck given the sharp improvement in relations.
"We are on our way to ending the cold peace. We are on a completely different level of relations now," the envoy said.
Suleiman has been Egypt's pointsman in mediating between Israel and the Palestinians and is involved in reforming and training Palestinian security forces ahead of the pullout.
His visit comes four days before a trip to Israel by Egyptian Foreign Minister Ahmed Abul Gheit, which will coincide with an expected tour of the region by US Secretary of State Condoleezza Rice.
"We are on our way to ending the cold peace. We are on a completely different level of relations now"
Israeli ambassador to Egypt
On 21 June, Sharon is due to hold only his second meeting with Palestinian President Mahmoud Abbas since Yasser Arafat died in November.
An Israeli-Palestinian committee coordinating Israel's withdrawal from the Gaza Strip met for the first time on Tuesday amid army warnings it would suspend the operation if it came under fire.
An army spokeswoman said the 90-minute meeting took place in a "positive atmosphere".