ETS Europe, the company that is running the marking this year, said on its website that all scripts were due to be delivered to markers' homes by Wednesday.
Some markers began work on papers more than five weeks ago, shortly after the ends of key stage 2 and 3 tests for 11- and 14-year-olds had finished.
The National Assessment Agency, which is overseeing the marking, said some papers being sent to examiners this week had been "reallocated" from other examiners who may have dropped out of the marking process.
All marking is supposed to be finished by Monday for the key stage 3 tests and Thursday for key stage 2, so test papers can be returned to schools by July 8.
It is not clear how long each marker will take to get through any extra allocation sent this week. However, some examiners said they felt it was unlikely the deadline would be met.
There have now been more than 7,000 comments posted on The TES online staffroom about this year's marking, many hostile.
Concerns have ranged from confusion surrounding examiner training to problems with computerised marking exercises and erratic delivery of scripts. Some senior markers have also said they were concerned about the quality of marking.
A key stage 2 English marker from the West Midlands said she was originally allocated 12 schools to mark. After waiting a month, scripts from only five of them had arrived. ETS then called her to say the other seven had been reallocated. Later in the day, another ETS employee emailed to ask when she would finish marking the remaining seven schools.
A spokesman for the National Assessment Agency said: "We have been given assurances by ETS that all scripts will be returned to schools by July 8. We are keeping a close eye on it, and all the indications thus far are that the marking is going to schedule."