The clash began when Pakistan refused to stop construction of a security gate to stop illegal crossings.
A Pakistan army Major and an Afghan border guard were killed in the clashes on Torkham border crossing on Sunday.
The Foreign Office (FO) said the delegation is coming in response to an invitation by Advisor to the Prime Minister on Foreign Affairs Sartaj Aziz.
"An Afghan delegation led by Deputy Foreign Minister Hekmat Khalil Karzai will visit Islamabad on Monday for discussions on the issues relating to Torkham border crossing as well as other matters pertaining to border management," the Foreign Office said.
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The border was closed six days ago and was reopened today after talks between the security officials of the two sides.
Pakistan has announced that no one will be allowed to enter through Torkham without valid documents from June 1.
After the border's reopening, only those carrying visa and entry permits would be allowed to enter Pakistan.