Sharif and President Hassan Rouhani met briefly for lunch, and will hold more in-depth talks on "bilateral issues and the expansion of economic cooperation," the official IRNA news agency reported.
During his two-day visit Sharif, who is accompanied by senior advisers, is also expected to meet supreme leader Ayatollah Ali Khamenei, Iran's ultimate authority, media reported.
As he met Sharif, Rouhani said Iran was ready to develop "road and railway networks between the two countries... As well as electric grids" in order to bolster economic ties, IRNA said.
Tehran says the soldiers -- four of whom returned home after being held for two months -- were taken across the border, a claim Islamabad denies.
More From This Section
The fate of the fifth soldier is unknown. His abductors claim to have killed him but this has yet to be officially confirmed.
Ties between Islamabad and Tehran have also been strained following the announcement in February by the Sharif government that Pakistan was suspending work on a USD 7.5-billion pipeline for Iranian gas exports.
IRNA quoted Sharif as saying Sunday that his government "is determined to remove obstacles" in the way of the gas pipeline. He did not elaborate.
He also said that Islamabad would cooperate with Tehran "to eliminate Jaish-ul Adl" or Army of Justice in Arabic, the Sunni rebel group that had captured the soldiers, IRNA said.
The group, active in the restive southeastern Sistan-Baluchestan province, took up arms in 2012 to fight for what it says are the rights of Iran's minority Sunni population.
IRNA reported that several protocol agreements would be signed during Sharif's visit.
It quoted Rouhani as saying that Iran hoped cooperation with Pakistan would reach "a superior level".