On social media such as Facebook and Twitter, which were still accessible using intermittent Wi-Fi access in the capital, Lome, users called for services to be restored.
In a statement on Wednesday, the Internet Without Borders group called the shutdown “an attack on Togolese citizens’ freedom of expression online”.
Amnesty International’s Togo director, Aime Adi, told AFP by telephone that the internet and mobile phone networks were completely off on Thursday in several cities in northern Togo.
Information minister Gilbert Bawara told several local radio stations on Wednesday evening that the government reserved the right to impose restrictions on access to the internet.
Amnesty’s Adi estimated that at least 100,000 opposition supporters marched against the government in Lome and several other cities across the country on Wednesday.
Other opposition figures put the number at one million.
The demonstrators want constitutional reform, including a limit on presidential mandates to two, five-year terms, and a two-round voting system.