Karzai told reporters he did not know about the specific allegations in the New York Times report but he defended Kabul's attempt to target the problem.
"Without a doubt, some Afghans are drugs smugglers, but the majority of them are the international mafia who do not live in Afghanistan," he said.
Drug production has skyrocketed since the US-led invasion that ousted the Taliban in 2001.
In 2007, nearly 200,000 hectares of land in Afghanistan was used to cultivate poppy - more than double the area in 2003 – and the country produced 93 per cent of the world's supply of opium, the raw material of heroin.
Schweich also said that the Taliban fighting Karzai's government profited from drugs, but Karzai was reluctant to move against big drug lords in his political power base in the south, where most of the country's opium and heroin is produced.
"Karzai was playing us like a fiddle," Schweich wrote.
"The US would spend billions of dollars on infrastructure development; the US and its allies would fight the Taliban. Karzai's friends could get richer off the drug trade," he wrote.
"Karzai had Taliban enemies who profited from drugs but he had even more supporters who did."
Schweich also accused the Pentagon and some US generals of obstructing attempts to get military forces to assist and protect opium crop eradication drives.
Nato and US military commanders have been reluctant to get involved in the drug fight, arguing that destroying farmers' crops would alienate tribesmen and increase support for the Taliban.
|International troops claim Taliban fighters are funded by the drugs trade in Afghanistan [AP]
Hillary Mann Leverett, a former US National Security Council official for Afghanistan, told Al Jazeera that the US knew that government ministers in Afghanistan, including the minister of defence in 2002, were involved in drug trafficking.
"When I worked on this issue at the White House in 2001 and 2002, we were made aware, very clearly aware, that the highest government officials, including the minister of defense at the time, were drug traffickers ... and there was a serious question of what would we do, how would we get aid into Afghanistan, deal with this Afghan government.
The report also points out that instead of fighting drugs and corruption, Karzai appointed Izzatulla Wasifi – a convicted heroin dealer - to his inner circle in government, as anti-corruption committee head.
Afghan ministers at that time had little expertise but were appointed because "they were warlords, they were thugs, they represented various ethnic and sectarian constituencies", Mann Leverett said.
She added that the US government chose to work with them in an attempt to stop Afghanistan becoming a haven for al-Qaeda.
"Instead of funding the warlords we could have funded the UN to have a security peacekeeping force throughout the country.
Another claim made in the New York Times article is that Ahmad Wali, Karzai's brother, is directly involved in the drugs trade in southern Afghanistan.
Al Jazeera's James Bays, reporting from Kabul, said Wali had denied the claims, saying they were politically motivated.
He said Wali told him he had been "putting up wth these smears for nearly seven years ... and when someone wants to get at the president, they come after me".
Gonzalo Gallegos, a state department spokesman, did not directly address Schweich's allegations but defended US policy and backing for Karzai.
"We know and understand that there is a corruption issue in Afghanistan but we're working with the sovereign government," Gallegos said on Thursday.
"President Karzai has shown us through word and deed that he is working with us to help improve the plight of that country."
Gallegos added that corruption was a deeply rooted problem and solving it would take time.