Baradar was released from jail in Pakistan as part of efforts to kick-start Afghanistan's peace process, but he has since been kept under house arrest, reportedly in Karachi or Peshawar, to the fury of Afghanistan.
"We will look for explanations from the Pakistan government for the exact whereabouts of Mullah Baradar and how can Pakistan facilitate direct talks between Mullah Baradar and the High Peace Council," Karzai's spokesperson Aimal Faizi told AFP.
The High Peace Council is the Afghan body charged with opening negotiations with the Taliban insurgents as US-led NATO forces prepare for withdrawal from the country by the end of next year.
Afghan officials believe that Baradar, who had been held in jail in Pakistan since 2010, could encourage Taliban leaders to seek a negotiated settlement to end the 12-year insurgency if he were fully at liberty.
About 400 Afghan soldiers or policemen die every month fighting the militants.
"Prime Minister Nawaz Sharif promised the release of Mullah Baradar, which they did, but Mullah Baradar is still under very strict supervision by Pakistan authorities," Faizi said.
Karzai, Sharif and British Prime Minister David Cameron will meet on Tuesday for the fourth trilateral summit designed to foster stability in the volatile south Asia region.
Apparent headway between then-Pakistani president Asif Ali Zardari and Karzai at the last summit hosted by Cameron in February quickly unravelled in a series of public rows.
"There have been ups and downs in the past but that should not stop us from working with Pakistan," Faizi said late Saturday.
"The focus of the meeting will be Pakistan support for the Afghan peace process, fighting terrorism and extremism, and Pakistan support for the security of the Afghan 2014 election."
He said Afghanistan expected Pakistan to stop militants crossing the border to launch attacks in the run-up to the April presidential elections for Karzai's successor.
"Pakistan can play a role to maintain Afghanistan security for upcoming elections because these terrorists are coming from the other side of the Durrand Line (border) to Afghanistan," Faizi said.
Karzai, who must step down next year after serving two terms, will also give a speech at the World Islamic Economic Forum in London, and at the Oxford Union, the university's debating society, during his four-day visit.
The search for a peace deal in Afghanistan is urgent as 87,000 NATO combat troops prepare to withdraw next year and the national army and police take on the fight against insurgents.
A Taliban office in Qatar that opened in June was meant to lead to talks, but instead it enraged Karzai after it was styled as an embassy for a government-in-exile.
Pakistan was a key backer of the hardline 1996-2001 Taliban regime in Kabul and is believed to shelter some of the movement's top leaders.
Islamabad officials were not immediately available to comment on the London summit.
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@AR: He means to say that Pakistani terrorists are sheltering him, so give him to them to put a bullet across
@Ali: You are right, stop helping the sending of terrorists and that will facilitate sending back refugee's instead. You want to send militants and refugee's in at once is it?
Why is Karzai not asking Pakistan to hand over 3 million Afghan refugees back to him?
Hi Karzai! Is he not a terrorist? why not let him stay in jail?