Thich Nhat Hanh writes in his book Fear: Essential Wisdom for Getting Through the Storm :

A mantra is a kind of magic formula that, once uttered, can entirely change a situation. It can change us, and it can change others. But this magic formula must be spoken in concentration, with body and mind focused as one. What you say in this state of being becomes a mantra.
…and about relationships: “to love without knowing how to love wounds the person we love.”

He clarifies that Mantras can be done across distance, across phone lines and screens and do not requiring the actual presence of the beloved.

He roots this transmutation practice in four mantras “effective for watering the seeds of happiness in yourself and your beloved and for transforming fear, suffering, and loneliness.”

First Mantra - Mantra for Offering Your Presence

When you love someone, the best thing you can offer that person is your presence. How can you love if you are not there? Come back to yourself, look into [their] eyes, and say, “Darling, you know something? I’m here for you.” You’re offering [them] your presence. You’re not preoccupied with the past or the future; you are there for your beloved. You must say this with your body and with your mind at the same time, and then you will see the transformation.

Second Mantra - Mantra for Recognizing Your Beloved

“Darling, I know you are there, and I am so happy.”
To be there is the first step, and recognizing the presence of the other person is the second step. Because you are fully there, you recognize that the presence of your beloved is something very precious. You embrace your beloved with mindfulness, and he or she will bloom like a flower. To be loved means first of all to be recognized as existing.

Third Mantra - Mantra for Relieving Suffering

Even before you do anything to help, your wholehearted presence already brings some relief, because when we suffer, we have great need for presence of the person we love. If we are suffering and the person we love ignores us, we suffer more. So what you can do — right away — is to manifest your true presence to your beloved and say the mantra with all your mindfulness: “Dear one, I know you are suffering. That is why I am here for you.” And already your loved one will feel better.

Your presence is a miracle, your understanding of his or her pain is a miracle, and you are able to offer this aspect of your love immediately. Really try to be there, for yourself, for life, for the people you love. Recognize the presence of those who live in the same place as you, and try to be there when one of them is suffering, because your presence is so precious for this person.

Fourth Mantra - Mantra for Reaching Out to Ask for Help

Thich Nhat Hanh notes, this is the most difficult of the four, for it exposes our greatest vulnerability while it pushes us to lean on our most paralyzing crutch.

This mantra is for when you are suffering and you believe that your beloved has caused you suffering. If someone else had done the same wrong to you, you would have suffered less. But this is the person you love the most, so you suffer deeply, and the last thing you feel like doing is to ask that person for help… So now it is your pride that is the obstacle to reconciliation and healing. According to the teaching of the Buddha, in true love there is no place for pride.

When you are suffering like this, you must go to the person you love and ask for his or her help. That is true love. Do not let pride keep you apart. You must overcome your pride. You must always go to him or her. That is what this mantra is for. Practice for yourself first, to bring about oneness of your body and mind before going to the other person to say the fourth mantra: “Dear one, I am suffering; please help.” This is very simple but very hard to do.

Resources

Brené Brown - The Power of Vulnerability : Connection is … what gives purpose and meaning to our lives. Connection, the ability to feel connected, -- neurobiologically that's how we're wired -- it's why we're here.

Louis Carter - 5 Tips to Build Better Personal Connections