Microsoft’s disdain for Google doesn’t extend to all of its rival’s products.

In a rare bit of cooperation, Microsoft’s Outlook.com is giving users of its free email service the option of logging into Google Chat to exchange instant messages and engage in audio or video conversations.

The tie-in announced on Tuesday represents an uneasy alliance in the midst of a typically contentious relationship between Microsoft Corp. and Google Inc.

Microsoft is framing its embrace of Google Chat as an example of how it’s trying to help connect people who rely on various services to interact with one another. Both Outlook.com and Google Chat are offered for free as way for Microsoft and Google to attract more online traffic to its advertising-supported services.

With the latest addition, Outlook.com accountholders will have three different ways to interact with their friends and family in real-time discussions. They have already been able to use Microsoft’s own Skype chat service and Facebook’s messaging service. Microsoft closed its Messenger chat service earlier this year as part of a switchover to Skype, which the company bought for $8.5 billion in 2011.

Even as it offers Google Chat to its Outlook.com users, Microsoft is warning consumers that Google’s search engine and other services can’t be trusted. The company has spending millions of dollars on a series of critical ads that began appearing online, in print and on television about six months ago.

Some of Microsoft’s recent advertising attacks have been aimed at Google’s Gmail, the foundation for Google Chat.

In a marketing campaign dubbed “Scroogled,” Microsoft lambastes Gmail for scanning the texts of emails to decipher what’s being discussed so ads on related topics can be displayed alongside the electronic conversations. While depicting Google as an obnoxious snoop, Microsoft’s ads urge people to switch to the less intrusive approach of Outlook.com.

Since the service’s debut nine years ago, Google has never tried to conceal that it uses computers to parse the discussions within Gmail correspondence.

No ads are shown in live discussions on Google Chat, but marketing messages can be displayed if the conversations are saved, according to Google’s policies. As it does with Gmail, Google’s computers scan the context of the saved chats to help pick out which ads to show.

That practice didn’t deter Outlook.com from linking up with Google Chat.

“We do not have any queasiness about adding Google Chat,” said Dharmesh Mehta, Outlook.com’s senior director. “We think it’s important to give people choice so they can make their email more personal. It also gives people one more reason to switch from Gmail to Outlook.com.”

Microsoft believes it already has dented Gmail since it converted its Hotmail.com users and other email accounts operated under other domain names, such as MSN.com, to Outlook.com earlier this year.

The company, which is based in Redmond, Washington, says it now has about 400 million Outlook.com users. That’s up from about 360 million users of Outlook.com and the Microsoft’s other webmail services three months ago.

Google, which is based in Mountain View, California, says it has more than 425 million Gmail users.