Tahiri, a member of the ruling Socialist Party, denies the allegations and called on prosecutors to investigate his detractors.
The calls for Tahiri to quit came on Monday after a TV interview with police officer Dritan Zagani, who was arrested on May 2 on suspicion of leaking information about police operations to drug smuggling gangs.
Zagani told journalists he had uncovered a chain of drug dealers trafficking marijuana, mostly from the southern Albanian village of Lazarat to Greece and Italy.
After conducting a secret investigation he forwarded information, including the phone numbers of drug dealers, to the central police office in Tirana. They responded to say the office checked the numbers, but that they did not work.
According to Zagani, a person from this office then tipped the trafficking group off that they were the target of a police probe.
Zagani claims to have found that top officials within the Interior Ministry, including Tahiri, were linked with the drug trafficking group.
At this point, Zagani said, he realised that he would then be scapegoated and accused himself of colluding with the drug trafficking group.
The allegations against Tahiri are only one of the worries of the ruling Socialist Party this week.
On Monday, Socialist Party lawmaker Arben Ndoka resigned over revelations that he had in 2003 been given a seven-and-a-half year prison sentence in Italy for human trafficking.
Balkan Insight reports that Ndoka was transferred to a prison in Albania where a court cut his sentence, freeing him in under three years.
In an open letter to fellow MPs, Ndoka claimed that the woman that accused him of trafficking, his brother's fiancee, staged her own kidnapping.
The allegations against Ndoka were, as with Tahiri's case, voiced by the opposition. In July 2014, Democratic Party MP Genc Strazmiri addressed Parliament over Ndoka's past. Ndoka later assaulted Strazmiri. Albania's High Court said the assault was outside of its purview to convict, since it took place within Parliament.
Also on Monday, another Socialist Party lawmaker's immunity from prosecution was lifted after he was arrested at the weekend.
Prosecutors suspect that Armando Prega shot and injured a fisherman during a brawl over fishing rights to a local lagoon.
On Tuesday the US Embassy in Tirana praised both Ndoka's decision to resign and the Parliament's decision to lift Prega's immunity.
