The video-sharing website YouTube has offered to show Thailand how to block material deemed insulting to King Bhumibol Adulyadej.
The ban on YouTube has been criticised by some rights groups
Thailand has banned the whole YouTube site over a slideshow and at least two other clips mocking the monarch.
YouTube executives said they would not take down material that did not violate policies but would show authorities how to block individual items.
Criticising or offending the monarchy is a serious crime in Thailand.
YouTube's head of global communications, Julie Supan, said it would prefer Thailand to have the power to remove items rather than have the whole site blocked.
The issue of lese majeste, or crimes of offending the monarchy, flared with last week's jailing of a Swiss man for 10 years for vandalising portraits of the king.
The world's longest-reigning monarch, 79-year-old King Bhumibol Adulyadej, is revered across Thailand, with some people even seeing him as a virtual god.
The first video, posted on Thursday, featured images of the king covered with graffiti, and juxtaposed pictures of feet over his face - an offensive act to Thais, who consider feet the dirtiest part of the body.
The clip was withdrawn but was followed by two similar clips.
Minister of Information Sitthichai Pookaiyaudom said Thailand would consider ending the ban when it had the ability to block all offending pages.
He said: "I don't want to hear a lecture on free speech... I am a proponent of free speech but this is just culturally insensitive and offensive... we will not tolerate materials that offend the monarchy."
Ms Supan said: "It's up to the Thailand government to decide whether to block specific videos, but we would rather that than have them block the entire site."
Thailand's decision to block YouTube, owned by Google, has drawn sharp criticism from media rights groups, who say it highlights an increasing amount of censorship by the military-backed government which came to power after September's coup.