He was scheduled to meet with Iranian President Hassan Rouhani on Monday.
Tehran has stepped up security along its long border with Pakistan after a suicide bomber killed 27 members of Iran's elite Revolutionary Guards in mid-February in southeastern Iran, with Iranian officials saying the attackers were based inside Pakistan.
"The prime minister's visit to Iran will further strengthen the bilateral relationship between the two countries", it added.
For its part, Tehran routinely alleges that Jaish-e-Adl, a dissident Sunni militant organization of Iranian Baluch, uses hideouts on Pakistani soil to orchestrate "terrorist" violence in its border region known as Sistan-Baluchistan.
Qureshi also called on Afghan government to take action against those militants hiding in Afghanistan and carry out terror attacks in Pakistan.
Meanwhile, predominantly Shia Muslim Iran says armed groups operate from safe havens in Pakistan and has repeatedly called on Islamabad to crack down on them.
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It remains to be seen whether Pakistani leader Khan could convince Iranian authorities that his country would not undermine Tehran's interests in the region.
Among them 10 were from Pakistan Navy, three from Air Force and one was a coastal guard, he added. "We intend to seal this whole border which spreads to 950 kilometres, gradually".
"Strongly condemning the recent terrorist attack in Pakistan, just as PM Imran Khan embarks on his first, historic visit to Iran. BRAS, which is the alliance of three Baloch terrorist organisations, has claimed responsibility for this terrorist act".
Militants carried out a deadly attack against Pakistani armed forces travelling in buses in Balochistan province.
"The Ministry of Foreign Affairs of the Islamic Republic of Pakistan avails itself of this opportunity to renew to the esteemed embassy the assurances of its highest consideration", the letter concluded.
He said Baloch insurgent groups had accepted responsibility for the incident and added the areas where such elements are trained had been identified and that Iranian authorities have been informed about such areas. Pakistan has generally tried to maintain close ties with both Saudi Arabia and Iran - bitter regional foes - but has drifted away from Tehran in the past few years. "Terrorists, extremists & their sponsors are terrified by close relations between Muslim states", he continued. He explained that in addition to deploying additional forces and helicopter surveillance, Pakistan already has begun fencing the "most vulnerable" portions of the border with Iran.