However, there was no immediate confirmation from the government or RIM that services had been blocked.
The Canada-based phone company and the Saudi government, which says that the Blackberry does not meet "regulatory requirements", were reportedly meeting to discuss how the dispute over access to data could be resolved.
"RIM showed on Thursday a degree of flexibility that has not been there over the past three months," a source close to the Saudi negotiations told the Reuters news agency.
"Progress is being made. We started debating the technicalities of new setups."
Regulators had earlier in the week ordered the kingdom's three mobile phone providers to block Blackberry services from Friday or face a $1.3m fine.
The United Arab Emirates also announced planson Sunday to block BlackBerry email, web browsing and messaging services in October if RIM did not comply with "local laws".
Blackberry information, such as emails and text messages, is stored in encrypted form on servers in Canada, where RIM is based, meaning that many government agencies are unable to access the information.
India, Lebanon, Algeria and Indonesia have all raised similar national security concerns about their lack of access to Blackberry data.
RIM and those foreign governments need to find a way to rework the balance between privacy and accessibility, Philip Victor, a data security advocate, told Al Jazeera.
"How do we ensure the bad guys aren't using it for purposes that could harm the country," he said.
However, authorities in the US can access BlackBerry users' information with a court order, and the UAE is pushing for the same powers.
Peter Van Loan, the Canadian trade minister, told reporters that his country's officials are working with foreign governments to find a solution, while Hillary Clinton, the US secretary of state, said the US would hold talks with the UAE and other countries on the issue.
The UAE and Saudi Arabia combined make up only around 1.2 million of RIM's more than 41 million subscribers, but some analysts said they were concerned about the impact on the company's reputation for providing iron-clad privacy.
"The company has to stand its ground ... they've built their loyalty largely around security," Nick Agostino, an analyst at Mackie Research Capital Corp., told the Reuters news agency.
But shares in the company slipped again on Thursday by $1.16, or 2.2 per cent, to $52.23, on the Nasdaq Stock Market.
The value of RIM's stock has fallen 23 per cent this year, and as the list of countries with concerns about access to Blackberry data grows, bans may affect a sizeable slice of BlackBerry customers.
However, some analysts said that with new technologies being developed all the time it would be difficult for government's to make a real impact on the control of the information being accessed by their citizens.
"I think their expectations are unrealistic over the long term to maintain the kind of control that they're looking for," Kevin Restivo, a senior mobile phone analyst at the technology research firm IDC, told Reuters.
"They're really trying to put the genie back in the bottle here".