(Other answer is a bit confusing, so writing instead of editing a lot)

Azure Functions can now run up to 10 minutes using the consumption plan by adding the functionTimeout setting to your host.json file:

In a serverless Consumption plan, the valid range is from 1 second to 10 minutes, and the default value is 5 minutes.

In both Premium and Dedicated (App Service) plans, there is no overall limit, and the default value is 30 minutes. A value of -1 indicates unbounded execution, but keeping a fixed upper bound is recommended

Source: https://learn.microsoft.com/en-us/azure/azure-functions/functions-host-json#functiontimeout

File: host.json

// Value indicating the timeout duration for all functions.
// Set functionTimeout to 10 minutes
{
    "functionTimeout": "00:10:00"
}

Source:

You can use regular App Service Plan, instead of a consumption plan to remove the timeout limit of 10 minutes forced on you on the cunsumption plan. The default is 5 minutes for consumption plan.

Indicates the timeout duration for all functions. It follows the timespan string format. In a serverless Consumption plan, the valid range is from 1 second to 10 minutes, and the default value is 5 minutes.

In the Premium plan, the valid range is from 1 second to 60 minutes, and the default value is 30 minutes.

In a Dedicated (App Service) plan, there is no overall limit, and the default value is 30 minutes. A value of -1 indicates unbounded execution, but keeping a fixed upper bound is recommended

https://learn.microsoft.com/en-us/azure/azure-functions/functions-host-json#functiontimeout

From your comments it looks like breaking up into smaller functions or using something other than functions isn't an option for you currently. In such case, AFAIK you can still do it with v2.0 as long as you're ready to use "App Service Plan".

The max limit of 10 minutes only applies to "Consumption Plan".

In fact, documentation explicitly suggests that if you have functions that run continuously or near continuously then App Service Plan can be more cost-effective as well.

You can use the "Always On" setting. Read about it on Microsoft Docs here.

Azure Functions scale and hosting

Also, documentation clearly states that default value for timeout with App Service plan is 30 minutes, but it can be set to unlimited manually.

Changes in features and functionality

UPDATE

From our discussion in comments, as null value isn't working for you like it did in version 1.x, please try taking out the "functionTimeout" setting completely.

I came across 2 different SO posts mentioning something similar and the Microsoft documentation text also says there is no real limit. Here are the links to SO posts I came across:

• SO Post 1
• SO Post 2

For now, host.json is the only way I know to change the timeout. So if you could change it cause the read only mode, there are two ways to edit.

One is use App service Editor to edit it, another is go your Function kudu site, under wwwroot folder edit the host.json file.

Note: From the doc and the answer by David we could know,

There is a 230 second (i.e. a little less than 4 mins) timeout for requests that are not sending any data back. After that, the client gets the 500 you saw, even though in reality the request is allowed to continue server side.

May be this is because of the plan that you are using , If you're using the Consumption plan, the default timeout is 5 minutes, but you can increase it to a maximum of 10 minutes. The maximum timeout on a Premium plan is 60 minutes. You can set your timeout as long as you want if you have a dedicated App Service plan.

functionTimeout property should be on top level, not under queues:

{
  "queues": {
    "maxPollingInterval": 2000,
    "visibilityTimeout": "00:00:30",
    "batchSize": 16,
    "maxDequeueCount": 3,
    "newBatchThreshold": 8
  },
  "functionTimeout": "00:10:00"
}

Thank you Jerry Liu posting your suggestion as an answer to help other community members.

"It is expected. Http request has a fixed timeout setting on Azure site. See Azure Web App timeout setting of 230s. In this aspect, there's no difference between Azure Web app and Http trigger Azure Function.

There is a 230 second (i.e. a little less than 4 mins) timeout for requests that are not sending any data back. After that, the client gets the 500 you saw, even though in reality the request is allowed to continue server side.

As for how to bypass this limitation, if it's not necessary to get an immediate feedback like httpresponse, you can use queue trigger to do your job.

Otherwise, have a look at Durable function. You could send an http request to start an orchestrator and get a response that it starts successfully and so on. The work is being processed in orchestrator and activity function and we don't need to worry about time out(as they are non-http trigger as well)."