The airline also suspended flights to Iran amid reports of an Israeli strike
Misbah-ul-Haq's request comes two days before Pakistan takes on Sri Lanka in a series of three one-day internationals, the first in the country for four years, and as many Twenty20 internationals.
The Sri Lanka team was attacked in Lahore in 2009 and since then most international teams have refused to tour the South Asian country, leaving Pakistan to play nearly all their "home" games in the United Arab Emirates.
Zimbabwe was the first country to return in 2015, with Pakistan hosting the West Indies, Sri Lanka, and a World XI team since then.
The current series was hit by withdrawals of ten top Sri Lankan players over security fears but Sri Lanka's cricket board received the all-clear from the defence ministry last week.
"Cricket world need to do more, not only for Pakistan but for any country where it is hit," said Misbah, under who Pakistan plays the first one-day international on Friday.
The remaining two matches will also be held in Karachi on Sunday and Wednesday.
The three Twenty20 internationals will be in Lahore on October 5, 7 and 9.
Misbah never captained any of his 56 Tests in Pakistan and he praised Sri Lanka - who arrived under heavy security - for the tour.
"I know it would have been a tough decision for Sri Lanka to tour," he said.
"Pakistan is a cricket-loving country and it would be injustice to deprive them of international cricket, so I hope that the world will support us more and more."
It had been ten years since the attacks, Misbah said, adding he hoped more international teams would consider touring his nation and others like Pakistan.
"Otherwise the survival of cricket will be difficult."
Misbah said his team - the majority of who will be playing a one-day international at home for the first time - were excited for the match.
Skipper Sarfaraz Ahmed, Babar Azam, Haris Sohail, and Wahab Riaz have featured in an ODI in Pakistan before.
"It's a special moment for all of us and players are excited as well as emotional, playing before their home fans and at home ground, so it's really special."
Misbah said Sri Lanka's top players should have come for the limited-overs series in Pakistan after being assured of head-of-state-like security by the government.
Ten of Sri Lanka's best players pulled out of the three-match ODI series and three Twenty20s in Pakistan due to security concerns - including ODI captain Dimuth Karunaratne and Twenty20 captain Lasith Malinga.
The airline also suspended flights to Iran amid reports of an Israeli strike
Expect fair to partly cloudy conditions today with chances of fog and mist formation in some areas
Iran fired air defense batteries after reports of explosions near a major airbase at the city of Isfahan
Other requests include residents seeking assistance with cleaning mud accumulation, restoring damaged furniture
Many students wade through waist-deep water to head to neighbour's house for online classes
With 30% of their inventory damaged, owners of Preloved Books now face the daunting task of rebuilding from scratch
Some doctors are already seeing more patients coming in with fever, diarrhoea, and dysentery
Five-time champions hold their nerve to claim victory by nine runs in the final over at Chandigarh