Java - alternative to thread.sleep

I have a requirement to pause a while loop for a specific number of milliseconds. I have tried using Thread.sleep(duration) but it is not accurate, especially in a looping scenario. Millisecond accuracy is important in my program.

Here is the algorithm where I don't want to go back to check for condition until expectedElapsedTime has passed by.

while (condition) {
    time = System.currentTimeMillis();
    //do something
    if (elapsedTime(time) < expectedElapsedTime) ) {
        pause the loop  // NEED SUBSTITUTE FOR Thread.sleep()
    }
    // Alternative that I have tried but not giving good results is 
    while ((elapsedTime(time) < expectedElapsedTime)) {
        //do nothing
    }
}

long elapsedTime(long time) {
   long diff = System.currentTimeMillis() - time;
   return diff;
}