The authorities deny such claims, but have not explained exactly why service has become slower.
Businesses, banks and even state organisations are not spared by the widespread disruption in the Internet, local media say.
"The Internet is in a coma," said the Ghanoon daily in a report in early this month.
"It only happens in Iran: the election comes, the Internet goes," it said, quoting a tweet in Farsi.
Facebook, Twitter, YouTube and numerous other sites, including thousands of Western ones, have been censored in Iran since massive street demonstrations that followed the re-election of President Mahmoud Ahmadinejad in 2009.
Those protests -- stifled by a heavy-handed crackdown that led to numerous arrests and even deaths -- were instigated online and observers say the authorities are choking the Internet to prevent a recurrence.
One DVD vendor, who sells illegal copies of Western movies downloaded online, said "you can forget about downloading stuff; the bandwidth drops every other minute."
A network supervisor at a major Internet service provider in Tehran said his company had been unable to address complaints about slower speeds, particularly accessing pages using the HTTPS secure communications protocol.
"Browsing (the net) is difficult due to the low speed. Even checking emails is a pain," he said.
"Sometimes, loading a secure Google page takes a few long seconds," he added.
Like others interviewed for this article, he did not want to be identified for fear of retribution.
The problem is not limited to slower speeds, but also affects what people can actually access in a country whose rulers take great care in seeking to ensure that people do not see or read things deemed to be inappropriate.
Earlier this month, an Iranian IT website reported that the last remaining software that enables users to bypass filters imposed on net traffic "has become practically inaccessible."
Among such software is the virtual private network (VPN), which lets people circumvent the filtering of websites.
VPN uses certain protocols to connect to servers outside Iran. In that way, the computer appears to be based in another country and bypasses the filters.
Blocking these protocols could theoretically contribute to slower speeds.
Use of VPN, or its sale, is illegal in Iran on the official grounds that it is insecure and allows access to material deemed as depraved, criminal or politically offensive.
Ramezanali Sobhani-Fard, head of the parliamentary communications committee, said VPN was blocked in early March, which has contributed to slowing the Internet, media reported.
He did not elaborate.
-- 'I cannot ignore the timing' --
Authorities refuse to officially confirm the new restraints, but former officials and media reports have accused the Supreme Council of Cyberspace of ordering them.
The council, set up in March 2012, is tasked with guarding Iranians from "dangers" on the Internet while enabling "a maximum utilisation of its opportunities."
The information and communication technology (ICT) ministry did not respond to AFP requests for an interview on the issue.
The complaints come as Iran prepares to elect its new president on June 14, but the authorities reject claims that there is any link with that and the current problems.
"Many parameters are involved in the Internet's speed, but the election drawing near is not one of them," a deputy ICT minister, Ali Hakim Javadi, said in early May.
His remarks have failed to allay concerns among an officially estimated 34 million net users out of a population of 75 million.
"Even if I wanted to believe it, I cannot ignore the timing," said Ali, a computer engineer.
The disruptions are also linked to Iran's stated plan of rolling out a national intranet that it says will be faster, more secure and clean of "inappropriate" content, observers say.
Critics say the unfinished "National Information Network" could expose Iranians to state monitoring once operational. They argue that a "National VPN" service launched in March could be a test run.
Users of the state-approved VPN service, available to select businesses reportedly at a monthly rate of 4,000,000 rials ($115, 88 euros), say it provides a relatively fast connection to select global websites.
The illegal VPN was available for as little as $50.
"You can actually get some work done with this VPN. But it is almost as if you are paying the government to spy on you," said one business user wary that his privacy could be violated.
The intranet could theoretically enable the regime to shut down the Internet at sensitive times, or effectively slow down it to a point where it is unusable.
But the authorities insist the network will co-exist with the Internet.
And a Tehran-based Western diplomat, speaking on condition of anonymity, was also skeptical.
"It is unlikely that Iran would implement more restrictions, as that would render its Internet inoperable to its people, businesses and even (governmental) organisations that heavily rely on it," said the diplomat.