The comments offered some hope that Iran and the US can end a stalemate that has in effect blocked the vital waterway, through which a fifth of global oil and liquefied natural gas flowed before the war.
Prospects for a deal had appeared to dim on Monday after the sides' latest remarks and demands.
In an interview with Bloomberg News, Pakistani Defence Minister Khawaja Asif said "things are shaping up again in favour of a peace arrangement or a deal".
"The signals in the last two three days are that we are close to some sort of an arrangement."
Iranian Foreign Minister Abbas Araqchi met Pakistani Interior Minister Mohsin Naqvi in Tehran on Tuesday, Araqchi's Telegram channel said on Tuesday, without providing further details.
Qatar's foreign ministry spokesman told a briefing earlier on Tuesday that separate discussions between Oman and Iran over management of the Strait of Hormuz were at an advanced stage.
The Iranian foreign ministry's Public Relations Office did not immediately respond to a call for comment.
Pakistan and Qatar have been the main mediators in the conflict in which thousands have been killed - mainly in Iran and Lebanon - since US and Israeli attacks on Iran on February 28.
Iran has hit back by striking US assets and infrastructure in countries including Oman, Jordan, Kuwait, Israel, the United Arab Emirates and Saudi Arabia.
Oil prices fell back on Tuesday after hitting a one-week high earlier in trading although it remains much higher than before the war.
Iranian officials said on Sunday they were nearing a final pact with Oman defining new shipping lanes in the Strait of Hormuz, which runs between them, but said that in itself would not open the waterway unless the US met certain conditions.
Those conditions were largely in line with a memorandum of understanding to end the conflict that was reached between the US and Iran in June and included compensation and an end to sanctions and military threats.
Iranian Foreign Minister Abbas Araqchi said on Sunday that Iran and the US were not holding direct talks but that messages were being exchanged through intermediaries.
Despite tentative signs of progress in diplomacy, there were reports of new attacks on shipping in the Gulf of Oman and the Red Sea, highlighting the widening threat to maritime trade.
Four crew members were killed in a suspected attack by Yemen's Iran-aligned Houthi rebels on a small cargo vessel in the Bab el-Mandeb strait on Tuesday, Yemen's transport ministry said.
The fatalities aboard the Egyptian-owned Tihamah, if confirmed, would be the first deaths in a Houthi strike on shipping since the Iran war began.
The Houthi militia have not claimed the attack.
A container ship was also hit by a missile off Pakistan, while sailing through the Gulf of Oman in a suspected US attack, sources said.
The Wall Street Journal reported a US official as saying that the ship had been hit by a US military helicopter after its crew ignored warnings from personnel working to enforce a naval blockade on Iranian ports.
