That's an opportunity to connect and start a conversation with that person. They want to know more about you. Your accent is a part of your identity, your background, your story. It's more important that you are understood when you speak, not that you have an accent. Again, you want your message to be clearly understood by your audience.
Listen to Albert Einstein's talk, "The Common Language of Science" which was aired as a radio broadcast to the London Science Conference on October 2, 1941. He talks about how science is an international language. He has a strong accent, but do you understand what he is saying? Does it interfere with the way you feel about him or his message?
There are some simple things you can do to improve your confidence and clarity when you speak. Here are some tips:
1. Think about what you are going to say, before you say it.
Fluency comes with preparation, rehearsal and experience, no matter what language you speak. For presentations, practice a minimum of speaking your topic at least 6 times so you're prepared. You spend hours on the Powerpoint. You need to spend time on the speech.
2. Speak more slowly.
Don't rush your words together. It's not a race. "Fast" does not mean "fluent." Take time to articulate the last consonant sound in each word. Use pauses between word groups, no more than seven words at a time. This allows the listener to keep pace with your speaking.
3.Practice the words and sounds that are difficult for you.
Make a list of your "high frequency" professional words you say all the time. Make sure you correctly articulate the sounds and put the stress on the correct syllable. Use dictionary.com to check your pronunciation. Spanish speakers, for example, need to watch their "V's" and not say "B" when they mean "V." In English the "V" is produced when the bottom lip vibrates when it makes contact with the top teeth.
4.Don't be lazy and skip over the consonant sounds.
Practice clear, crisp consonants like /t/, /d/, /p/, /b/,/k/, and /g/. Make sure you complete the longer nasal sounds of /n/, /m/, /ng/. Hold your tongue behind your top teeth for the dark /L/. And make sure you say every /rrrr/ in each word with a growl. Find words with those consonants and practice saying them ten times each to create a new habit when you speak.
5. Be yourself while you speak with confidence and clarity.
Be considerate of your audience. Focus on "how" clearly you speak the message. Take your time. If you're on the phone, don't multi-task. Pay attention to your listener. Ask if they understood you or you need to clarify the information. Numbers are especially difficult to understand over the phone. Remember, what you say has value. Communication is a two way street. It takes both people to make a conversation successful.